During the development of new products, manufacturers frequently rely on computer simulations to evaluate and refine the product design. For example, aerospace and automotive manufacturers rely on computational fluid dynamics (CFD) analysis to determine the interaction of fluids with the surfaces of an object. Manufacturers may also employ CFD analysis to analyze fluid processes such as cooling, mixing and heat transfer. In addition to CFD analysis, manufacturers may rely on computer simulations to evaluate the structural, acoustic and/or electromagnetic response of an object.
Computer simulations such as CFD analysis require the creation of a mesh or grid of elements on the surfaces of the object to be analyzed. For objects having high curvature in at least one direction, it is desirable that the grid is of relatively high resolution (i.e., a relatively fine mesh of grid elements) in the direction of high curvature in order to improve the degree of accuracy of the CFD solution. For example, the wing of an aircraft is generally straight along the leading edge with generally no curvature in the spanwise direction and therefore may require reduced grid resolution in the spanwise direction. However, in the chordwise direction, the wing has an airfoil shape with a relatively high degree of curvature at the leading edge such that the grid resolution at the leading edge along the chordwise direction is preferably higher than the grid resolution along the spanwise direction. Likewise, it is desirable that the grid has a relatively high degree of resolution in certain regions of interest of the object. For example, in the case of a wing, such regions of interest may comprise localized areas of the wing that may be subjected to shockwaves, vortices, localized flow separation and other phenomena.
The prior art includes several methods of generating a grid on an object. For example, one method automatically creates an isotropic grid across the surfaces of an object. Such method results in a grid having the same degree of resolution in all directions of the surface without regard to differences in curvature and without regard to regions of interest on the surfaces that may be subject to localized phenomena. Unfortunately, because of the unnecessarily high degree of resolution along directions of minimal curvature, CFD analysis using such a grid is computationally inefficient due to the relatively large quantity of elements that make up the total grid.
Another method of grid generation minimizes the quantity of elements along directions of low curvature while providing a relatively large quantity of elements along directions of high curvature. The method relies on manual insertion of rectangular grid elements in areas of high curvature or in regions or interest as a means to increase the grid resolution and improve the solution accuracy. Unfortunately, manual insertion of grid elements is labor intensive and can significantly add to the total amount of time required to generate a CFD solution.
A further approach to grid generation relies on automatic creation of anisotropic triangular grid elements having a relatively high aspect ratio in areas of high curvature or in regions of interest. Although the use of anisotropic triangular grid generation allows for control of the grid resolution in a desired direction, the quality of the grid suffers due to misalignment of the grid elements with the direction of curvature. For example, creation of an anisotropic triangular grid on a wing leading edge may result in elements that are misaligned with the direction of curvature which may reduce the accuracy of the CFD solution.
As can be seen, there exists a need in the art for a method for generating a grid on a surface of an object wherein the grid elements have relatively high resolution along directions of high curvature and relatively low resolution along directions of low curvature. Furthermore, there exists a need in the art for a method for generating a grid of high aspect ratio wherein the grid elements are generally aligned with the direction of curvature. Additionally, there exists a need in the art for a method for generating a grid wherein the grid elements transition from high resolution to low resolution in correspondence with a reduction in the degree of curvature along a direction of the surface such as along a chordwise direction of an airfoil section.